If I am not a multiple of , then I am between and .
If I am a multiple of , I am between and .
If I am not a multiple of , I am between and .
What number am I?
Source: CMC Communicator Volume 29, No. 3 March 2005

SOLUTION
Not a multiple of between and :
Multiples of between and :
Not a multiple of between and :
We now examine each candidate number and look for those that pass all three conditions. When a number passes/fails a condition we mark it by a P/F in the following table